A passive location error distribution prediction method and device based on a conditional flow network architecture

Abstract

This invention discloses a passive positioning error distribution prediction method and device based on a conditional flow network architecture, relating to the field of passive positioning technology. The method includes: acquiring key parameters of a radar system; these key parameters include power, observation time, baud rate, target position coordinates, and receiver position coordinates; processing the key parameters of the radar system using a trained conditional normalized flow neural network model to generate a positioning error distribution; wherein the trained conditional normalized flow neural network model is trained using data of a preset category as training samples and the calculated positioning error as the true label of the training samples; and obtaining the conditional probability density of any positioning error value and various statistical indicators based on the positioning error distribution. This invention allows for flexible and efficient derivation of various indicators without repeated modeling.

Description

Technical Field

[0001] This invention belongs to the field of passive positioning technology, specifically relating to a passive positioning error distribution prediction method and device based on a conditional flow network architecture. Background Technology

[0002] Passive positioning technology has become a core technology in fields such as wireless sensing, radar systems, disaster relief, and medical monitoring, and has received considerable attention from academia and industry in recent years. Passive positioning technology achieves non-cooperative positioning by processing signals emitted or reflected by the target. It not only possesses inherent advantages such as strong concealment and low power consumption, but is also suitable for scenarios in complex environments where active signal sources cannot be deployed.

[0003] The existing technology has the following shortcomings: First, assess the diversity and specificity of the needs.

[0004] In different application scenarios (such as radar tracking, medical monitoring, and disaster relief), the focus of system evaluation varies greatly. Some focus on overall accuracy (RMSE), some on worst-case scenarios (maximum error), and some on boundary performance (95th percentile error). This evaluation requirement, which varies depending on the "scenario" and "user preferences," inevitably requires multiple performance metrics. Current technologies typically employ dedicated modeling for specific metrics, building separate mathematical models or predictors for each important performance metric; using theoretical tools such as the Cramer-Robb lower bound (CRLB) to provide a theoretical lower bound for the mean squared error (MSE) or RMSE of the unbiased estimator; or utilizing data-driven methods such as neural networks to directly learn the mapping relationship from system condition parameters to specific metrics (such as RMSE). However, these methods are essentially "one model for one metric." When the application scenario changes and another metric needs to be considered (e.g., from RMSE to 95th percentile error), the original model becomes completely invalid. Theoretical derivation or data collection and model training must be carried out again, which is cumbersome and costly. Providing only an isolated value cannot reveal the full picture of the error distribution (such as skewness, kurtosis, and tailing), which may mask the risks of the system under certain critical conditions.

[0005] Second, the inherent defects of traditional modeling methods.

[0006] The paradigm of single-indicator-single-model approaches dictates that current techniques typically establish a dedicated prediction model (e.g., based on CRLB or neural networks) for each specific indicator (such as RMSE). When a new or different indicator is needed, a new model must be designed and trained from scratch, resulting in significant repetitive work and computational overhead. Distribution modeling, which directly models the complete probability distribution of the error, addresses the flexibility issue at its root (since all indicators can be derived from the same distribution). However, traditional distribution modeling methods (such as Monte Carlo simulations) rely on generating massive amounts of samples and then using techniques like histograms or kernel density estimation (KDE) to approximate the overall error probability distribution. While histograms can accurately capture the shape of the distribution when the sample size is large enough, they require a large number of samples, thus incurring high computational costs. With insufficient sample size, histograms appear coarse and discontinuous, while KDEs exhibit large variance, leading to unstable and unreliable estimation results. Therefore, current methods generally suffer from insufficient flexibility and inefficiency in error distribution modeling.

[0007] In conclusion, constructing a theoretical and tool system capable of accurately modeling positioning error distribution and supporting the flexible extraction of various customized indicators is of vital importance for promoting the in-depth application of passive positioning technology in critical tasks. Summary of the Invention

[0008] To address the aforementioned problems in the existing technology, this invention provides a passive localization error distribution prediction method and apparatus based on a conditional flow network architecture. The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, the present invention provides a passive localization error distribution prediction method based on a conditional flow network architecture, comprising: Obtain key parameters of the radar system; key parameters include power, observation time, baud rate, target position coordinates, and receiver position coordinates; A pre-trained conditional normalized flow neural network model is used to process the key parameters of the radar system and generate a positioning error distribution. The pre-trained conditional normalized flow neural network model is obtained by training the initial conditional normalized flow neural network model with data of a preset category as training samples and the calculated positioning error as the true label of the training samples. Based on the positioning error distribution, obtain the conditional probability density of any positioning error value, as well as various statistical indicators.

[0009] Secondly, the present invention also provides a passive positioning error distribution prediction device based on a conditional flow network architecture, comprising: The data acquisition module is used to acquire key parameters of the radar system; these key parameters include power, observation time, baud rate, target position coordinates, and receiver position coordinates. The data processing module is used to process the key parameters of the radar system using a pre-trained conditional normalized flow neural network model to generate a positioning error distribution. The pre-trained conditional normalized flow neural network model is obtained by training the initial conditional normalized flow neural network model with data of a preset category as training samples and the calculated positioning error as the true label of the training samples. The results analysis module is used to obtain the conditional probability density of any positioning error value and various statistical indicators based on the positioning error distribution.

[0010] The beneficial effects of this invention are: This invention provides a passive positioning error distribution prediction method and apparatus based on a conditional flow network architecture. The conditional normalized flow neural network model introduces a hierarchical structure to extract geometric parameters from the geometric distribution and integrates environmental parameters as conditional inputs into the conditional normalized flow neural network model. Numerical experiments show that the model proposed in this invention can accurately approximate the distribution of positioning errors, thus enabling convenient and flexible prediction of positioning errors under various conditional parameters.

[0011] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0012] Figure 1 This is a flowchart of a passive localization error distribution prediction method based on a conditional flow network architecture provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a passive localization error distribution prediction method based on a conditional flow network architecture provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a fitting positioning error distribution provided in an embodiment of the present invention. Detailed Implementation

[0013] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0014] Please see Figure 1 , Figure 1 This is a flowchart of a passive positioning error distribution prediction method based on a conditional flow network architecture provided by an embodiment of the present invention. The passive positioning error distribution prediction method based on a conditional flow network architecture provided by the present invention includes: S101. Obtain key parameters of the radar system; the key parameters include power, observation time, baud rate, target position coordinates, and receiver position coordinates.

[0015] S102. The key parameters of the radar system are processed using a pre-trained conditional normalized flow neural network model to generate a positioning error distribution; wherein, the pre-trained conditional normalized flow neural network model is obtained by training the initial conditional normalized flow neural network model with data of a preset category as training samples and the calculated positioning error as the true label of the training samples.

[0016] Specifically, in this embodiment, a Conditional Normalized Flow Neural Network (CNF) model is constructed and trained to obtain a well-trained CNF model. During the inference process, the model processes key parameters of the radar system to generate a positioning error distribution. The well-trained CNF model possesses efficient error prediction and multi-dimensional result output capabilities. During the forward inference process, the model receives key parameters of the radar system. Then, the corresponding positioning error distribution can be directly generated. .

[0017] S103. Based on the positioning error distribution, obtain the conditional probability density of any positioning error value and various statistical indicators; among which, the various statistical indicators include, but are not limited to, key performance indicators such as root mean square error, average error, and 95th percentile error, to meet the evaluation needs of different application scenarios.

[0018] Specifically, in this embodiment, based on the positioning error distribution It can output results in various forms, namely: Probability density estimation: For any given error value, the model can accurately calculate its conditional probability density, providing a quantitative basis for the likelihood assessment of the error.

[0019] Statistical extraction: Through distribution sampling or analytical calculation, the model can flexibly output various statistical indicators, including but not limited to key performance indicators such as root mean square error (RMSE), mean error (ME), and 95th percentile error, to meet the evaluation needs of different application scenarios. Distribution visualization: The model supports the generation of complete error distribution curves, which intuitively show the central tendency, dispersion and distribution pattern of errors, providing a graphical reference for system performance analysis.

[0020] In summary, this invention provides a passive positioning error distribution prediction method based on a conditional flow network architecture. The conditional normalized flow neural network model introduces a hierarchical structure to extract geometric parameters from the geometric distribution and integrates environmental parameters as conditional inputs into the conditional normalized flow neural network model. Numerical experiments show that the model proposed in this invention can accurately approximate the distribution of positioning errors, thus enabling convenient and flexible prediction of positioning errors under various conditional parameters.

[0021] In an optional embodiment of the present invention, please refer to Figure 2 , Figure 2 This is a schematic diagram of a passive localization error distribution prediction method based on a conditional flow network architecture provided in an embodiment of the present invention. Training an initial conditional normalized flow neural network model includes: Data of a preset category is acquired as training and validation samples to construct training and validation datasets; the data of the preset category contains key parameters of the radar system. Obtain the true labels of the training samples in the training dataset and the true labels of the validation samples in the validation dataset; the true labels are obtained by calculating the localization error between the estimated position of the target and the target position. Input a portion of the samples from the training dataset into the first... The conditionally normalized flow neural network model to be trained is then trained to obtain the first... The prediction results output during this training process; According to the The prediction results output during the training process are the same as those during the training phase. The true labels of the training samples for the next conditionally normalized flow neural network model to be trained are used to calculate the loss and serve as the basis for the next training sample. Loss during each training session; According to the The loss from the training process is backpropagated to update the loss from the training process. The network parameters of the conditionally normalized flow neural network model to be trained are obtained. The system first trains a conditionally normalized flow neural network model. Then, at each preset validation interval, the validation samples in the validation dataset are input into the system to be trained to obtain the output prediction results. Combined with the true labels of the validation samples in the validation dataset, model selection and hyperparameter tuning are performed. This process is iterated until the number of training iterations or the degree of convergence meets the preset conditions, and a well-trained conditionally normalized flow neural network model is obtained.

[0022] In this embodiment, the key parameters of the radar system are initialized, including power, observation time, baud rate, target position coordinates, and receiver position coordinates, i.e., vectors. By reasonably initializing the parameters and setting a reasonable range for them, we can ensure the diversity and authenticity of the generated simulation data, and provide high-quality input features and error labels for subsequent model training.

[0023] In this embodiment, calculating the positioning error between the estimated target position and the target position includes: In the operational scenario of a radar system, a channel model and a received signal model are constructed; among them; In a simplified scenario, the transmitter and receiver are each equipped with only one antenna, and both ends are relatively stationary. A far-field, fast-fading wireless signal model is used to construct the channel model. In this case, the signal from the transmitter to the receiver... The signal model of a receiver can be represented as: ; The received signal model is represented as follows: ; in, Indicates the signal source to the first The complex channel gain of each receiver, Indicates amplitude, Represents the natural base. Represents the imaginary unit. Indicates phase, Indicates the receiving end The received signal, Indicates the time of the radiation source The transmitted signal, Indicates from the radiation source to the... Signal delay at each receiving end Indicates the first The noise at each receiver follows a zero-mean complex Gaussian distribution. Indicates the index of the receiving end. This indicates the total number of receivers.

[0024] In this embodiment, calculating the positioning error between the estimated position of the target and the target position further includes: The received signal is processed using a cross-correlation algorithm to calculate the Time Difference of Arrival (TDOA) at different receiving ends. The peak value of the cross-correlation function is then used as the delay between the received target signal and the target signal. Specifically: Radar systems use signal processing techniques to estimate the propagation time delay difference between the radiation source and different receivers. Indicates the first The first receiver and the first The time delay difference between each receiver is calculated. Since these delays cannot be directly observed, the system uses a cross-correlation method to process the received signal and calculate the time delay difference between the receivers. The received signal of the first receiver is the same as that of the second receiver. The estimated time delay difference between the received signals at each receiver is expressed as: ; in, , This represents an estimate of the time delay difference. Indicates the sampling frequency. Indicates the length of the signal sequence. Indicates the first The receiving end and the first The potential delay at each receiver (in units of sampling points) Indicates the first At that moment, Indicates complex conjugation.

[0025] It should be noted that the efficiency and accuracy of the cross-correlation algorithm in this stage directly determine the quality of TDOA data and lay the foundation for subsequent calculation of positioning error and model training.

[0026] In this embodiment, calculating the positioning error between the estimated target position and the target position further includes: Based on the estimated time delay difference, a set of equations is constructed. The location of the radiation source is obtained by solving the equations using the location information of each receiver. The set of equations is expressed as follows: ; in, Indicates the radiation source to the first The distance between the receivers Represents the speed of light. This represents the distance difference between the radiation source and the reference receiver relative to other receivers. This represents the delay difference between the radiation source and the reference receiver relative to other receivers. Indicates the location of the radiation source. Indicates the first The location of the receiving end; It should be noted that, in order to solve the above equations (which have high computational complexity due to their nonlinear characteristics), this embodiment uses the Chan algorithm. The Chan algorithm uses a double-weighted least squares method to solve for the target position, which can provide a non-recursive analytical solution while linearizing the nonlinear equations, thereby avoiding dependence on the initial estimate.

[0027] The estimated target position is obtained based on the distance difference between the radiation source and the reference receiver relative to other receivers; the positioning error between the estimated target position and the actual target position is calculated. As a real label, it is represented as: ; ; in, Indicates the target location. Indicates the estimated target location. Indicates power, Indicates the observation time. Indicates baud rate, Indicates the target location coordinates. Indicates the location coordinates of the receiving end. This represents data categorized by a preset category.

[0028] Furthermore, the objective of this embodiment is to establish a conditional probability distribution model for the positioning error, expressed as: ; in, It is a condition variable vector.

[0029] In this embodiment, the conditional normalized flow neural network model adopts a hierarchical invertible transformation architecture, which asymptotically maps the basic distribution to a complex conditional error distribution through a series of parameterized bijective transformations; each transformation module consists of two core components: The conditionally normalized flow neural network model includes an autoregressive rational quadratic spline flow layer that uses piecewise rational quadratic functions to achieve nonlinear transformations. This layer, through learnable node positions, function derivatives, and interval width parameters, enables fine-tuning of the probability density function locally, effectively capturing multimodal characteristics, asymmetric structures, and heavy tails that may exist in the error distribution. Its autoregressive structure ensures that the transformation of each dimension depends only on the previous dimension, guaranteeing both the invertibility of the transformation and effective modeling of complex dependencies. The conditionally normalized flow neural network model includes an LU linear permutation layer that achieves intelligent mixing of feature dimensions through invertible linear transformations based on LU decomposition. This design not only enhances the model's performance but also ensures efficient probability density correction through simplified determinant calculations. The alternation of linear and nonlinear transformations allows the network to gradually construct complex distribution patterns while maintaining invertibility.

[0030] In this embodiment, the transformation formula followed by the transformation chain of the conditionally normalized flow neural network model is expressed as follows: ; ; in, This represents a conditional probability distribution model constructed based on the positioning error. Represents the basic distribution. This represents the latent variable obtained through the inverse conditional transformation. Indicates the target location. Indicates the estimated target location. Indicates power, Indicates the observation time. Indicates baud rate, Indicates the target location coordinates. Indicates the location coordinates of the receiving end. This represents data categorized by a preset category.

[0031] It should be noted that the transformation formula is designed to ensure the differentiability of both bidirectional mappings from the latent space to the error space. This allows the model to generate error samples from latent variables through forward transformation and to calculate the log-likelihood of a given error through inverse transformation. During the training phase, network parameters are optimized by minimizing the forward KL divergence. During the inference phase, the trained CNF network can directly generate accurate error distributions for new systems and supports the efficient extraction of various statistics from them, completely avoiding the high computational overhead of traditional Monte Carlo methods.

[0032] In this embodiment, a portion of the samples from the training dataset are input to the first... Before training the conditionally normalized flow neural network model to be trained, the following steps are also included: The model consists of a system parameter vector containing key information such as power, delay, bandwidth, and geometric configuration. As conditional inputs, several of the input features are related to location parameters. To address the issues of high dimensionality and complexity, data from predefined categories are used. Target position coordinates Receiving end position coordinates Mapping to a single geometrical precision metric, GDOP, to quantify the impact of spatial geometry on positioning accuracy yields processed data categorized according to preset standards. Among them, geometric accuracy indicators Represented as: ; in, Represents trace operation. The configuration matrix represents the spatial relationship between the target and the receiver; that is, by using vectors Using this as network input to model the localization error distribution can significantly improve the model's adaptability and accuracy to changes in system configuration. This model is called a structured localization error network, and the distribution transformation is achieved through a carefully designed chain of transformation modules. The processed data of the preset categories is input into the conditionally normalized flow neural network model to be trained.

[0033] In this embodiment, the input feature vector The data generation relies on the Monte Carlo (MC) method, which estimates the probability distribution through repeated sampling. Specifically, given conditions... The localization algorithm will be executed multiple times to generate... One independent error sample: ; The data labels indicate that they were obtained from 500 Monte Carlo experiments, and the results were logarithmically processed to enhance numerical stability. For signal generation, the radiation source employed a binary phase-shift keying (BPSK) modulation scheme, and all modulated signals were precisely generated using the MATLAB communication toolbox.

[0034] For optimization, the Adam optimizer was selected for parameter updates, combined with cosine annealing to dynamically adjust the learning rate. This combination ensures rapid convergence in the early stages of optimization while enabling finer parameter tuning in the later stages of training. For network hyperparameters, a systematic grid search was implemented to determine the optimal configuration.

[0035] During training, the Kullback-Leibler divergence loss is monitored simultaneously on both the training and validation sets and used as a key performance indicator. An early stopping mechanism is employed to save the model parameters with the lowest validation loss; this optimal model will be used for subsequent testing and in-depth analysis. This rigorous training and validation process ensures that the model maintains excellent generalization ability while accurately capturing the complex statistical characteristics of passive localization errors.

[0036] To ensure the robustness of the model evaluation, a test dataset was also provided, which was divided into training, validation, and test sets in a 6:3:1 ratio. Please see [link to relevant documentation]. Figure 3 , Figure 3 This is a schematic diagram of a fitting positioning error distribution provided in an embodiment of the present invention. Figure 3 This provides an intuitive comparison, demonstrating how different methods fit the localization error distribution under given parameters. The results clearly show that CNF provides the best fit to the error distribution. This improvement primarily stems from effective feature dimensionality reduction, which enables the network to learn the mapping relationship between spatial structure and error more efficiently, thereby enhancing the model's performance across various scenarios and parameter settings.

[0037] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0038] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0039] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A passive localization error distribution prediction method based on a conditional flow network architecture, characterized in that, include: Acquire key parameters of the radar system; these key parameters include power, observation time, baud rate, target position coordinates, and receiver position coordinates. The key parameters of the radar system are processed using a pre-trained conditional normalized flow neural network model to generate a positioning error distribution. The pre-trained conditional normalized flow neural network model is obtained by training an initial conditional normalized flow neural network model with data of a preset category as training samples and the calculated positioning error as the true label of the training samples. Based on the positioning error distribution, the conditional probability density of any positioning error value is obtained, as well as various statistical indicators.

2. The method of claim 1, wherein, Training the initial conditionally normalized flow neural network model includes: Data of a preset category is acquired and used as training and validation samples to construct a training dataset and a validation dataset; wherein, the data of the preset category are key parameters of the radar system; Obtain the true labels of the training samples in the training dataset and the true labels of the validation samples in the validation dataset; wherein, the true labels are obtained by calculating the positioning error between the estimated position of the target and the target position; Input a portion of the samples from the training dataset into the first... The conditionally normalized flow neural network model to be trained is then trained to obtain the first... The prediction results output during this training process; According to the The prediction results output during the training process are the same as those during the training phase. The true labels of the training samples for the next conditionally normalized flow neural network model to be trained are used to calculate the loss and serve as the basis for the next training sample. Loss during each training session; According to the The loss from the training process is backpropagated to update the loss from the training process. The network parameters of the conditionally normalized flow neural network model to be trained are obtained. The training process involves several steps: first, training a conditional normalized flow neural network model; second, training a conditional normalized flow neural network model by inputting validation samples from the validation dataset into the model at preset validation intervals to obtain the output prediction results; third, training a conditional normalized flow neural network model by combining the true labels of the validation samples from the validation dataset with the model selection and hyperparameter tuning; and fourth, training a conditional normalized flow neural network model by iterating until the number of training iterations or the degree of convergence meets preset conditions.

3. The method of claim 2, wherein, Calculate the positioning error between the estimated target position and the target position, including: In the operational scenario of a radar system, a channel model and a received signal model are constructed; among them; The channel model is represented as: ; The received signal model is represented as: ; in, Indicates the signal source to the first The complex channel gain of each receiver, Indicates amplitude, Represents the natural base. Represents the imaginary unit. Indicates phase, Indicates the receiving end The received signal, Indicates the time of the radiation source The transmitted signal, Indicates from the radiation source to the... Signal delay at each receiving end Indicates the first The noise at each receiver follows a zero-mean complex Gaussian distribution. Indicates the index of the receiving end. This indicates the total number of receivers.

4. The passive localization error distribution prediction method based on conditional flow network architecture according to claim 3, characterized in that, The calculation of the positioning error between the estimated position of the target and the target position also includes: The received signals from each receiver are processed using a cross-correlation method to calculate the first... The received signal of the first receiver is the same as that of the second receiver. The estimated time delay difference between the received signals at each receiver is expressed as: ； in, This represents an estimate of the time delay difference. Indicates the sampling frequency. Indicates the length of the signal sequence. Indicates the first The receiving end and the first Potential delay at each receiving end, Indicates the first At that moment, Indicates complex conjugation.

5. The passive localization error distribution prediction method based on conditional flow network architecture according to claim 4, characterized in that, Calculating the positioning error between the estimated target position and the target position also includes: Based on the estimated time delay difference, a set of equations is constructed. The location of the radiation source is obtained by solving the set of equations using the location information of each receiver. The set of equations is expressed as follows: ； in, Indicates the radiation source to the first The distance between the receivers Represents the speed of light. This represents the distance difference between the radiation source and the reference receiver relative to other receivers. This represents the delay difference between the radiation source and the reference receiver relative to other receivers. Indicates the location of the radiation source. Indicates the first The location of the receiving end; According to the distance difference between the radiation source and the reference receiving end relative to other receiving ends, an estimated target position is obtained; and a positioning error between the estimated target position and the target position is calculated is expressed as: ； ； in, Indicates the target location. Indicates the estimated target location. Indicates power, Indicates the observation time. Indicates baud rate, Indicates the target location coordinates. Indicates the location coordinates of the receiving end. This represents data categorized by a preset category.

6. The method of claim 2, wherein, The conditional normalized flow neural network model employs a hierarchical invertible transformation architecture, asymptotically mapping the basic distribution to a complex conditional error distribution through a series of parameterized bijective transformations; wherein... The conditionally normalized flow neural network model includes an autoregressive rational quadratic spline flow layer that uses piecewise rational quadratic functions to achieve nonlinear transformation. The conditionally normalized flow neural network model includes an LU linear permutation layer that achieves intelligent mixing of feature dimensions through an invertible linear transformation based on LU decomposition.

7. The method of claim 6, wherein, The transformation formula followed by the transformation chain of the conditionally normalized flow neural network model is expressed as follows: ； ； in, This represents a conditional probability distribution model constructed based on the positioning error. Represents the basic distribution. This represents the latent variable obtained through the inverse conditional transformation. Indicates the target location. Indicates the estimated target location. Indicates power, Indicates the observation time. Indicates baud rate, Indicates the target location coordinates. Indicates the location coordinates of the receiving end. This represents data categorized by a preset category.

8. The method of claim 2, wherein, inputting part of the samples in the training data set into a first conditional normalization flow neural network model to be trained before training the part of the samples in the training data set, the method further comprises: Data of the preset category Target position coordinates Receiving end position coordinates Mapping to a single geometrical precision metric, GDOP, to quantify the impact of spatial geometry on positioning accuracy yields processed data categorized according to preset standards. ; wherein, the geometric accuracy index Represented as: ； wherein, denotes a trace operation, denotes a configuration matrix representing the spatial relationship between the target and the receiving end; The processed data of the preset categories is input into the conditionally normalized flow neural network model to be trained.

9. The method of claim 1, wherein, The statistical indicators include root mean square error, average error, and 95th percentile error.

10. A passive location error distribution prediction apparatus based on a conditional flow network architecture, characterized by, include: The data acquisition module is used to acquire key parameters of the radar system; these key parameters include power, observation time, baud rate, target position coordinates, and receiver position coordinates. The data processing module is used to process the key parameters of the radar system using a pre-trained conditional normalized flow neural network model to generate a positioning error distribution. The pre-trained conditional normalized flow neural network model is obtained by training an initial conditional normalized flow neural network model with data of a preset category as training samples and the calculated positioning error as the true label of the training samples. A result analysis module is configured to obtain a conditional probability density of any positioning error value and obtain various statistical indexes according to the positioning error distribution.

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